Solving the line planning problem with service-levels using a column generation-based heuristic algorithm

Abstract

This research investigates the strategic design of bus line networks by incorporating the operational objectives and constraints relevant to network operators. Drawing on industry expertise from a public transportation software company, we formulate the problem as a line planning optimization problem aimed at minimizing network operating costs while simultaneously addressing two critical service quality metrics: the deviation between passengers’ actual travel times and their respective shortest-path travel times, and the proportion of passengers completing trips without transfers. To address problem instances of realistic scale and complexity, we develop and implement a column generation heuristic framework wherein both bus lines and passenger routing paths are generated dynamically throughout the solution process. Our methodological approach combines column generation and column enumeration algorithms, demonstrating computational efficiency when evaluated against established benchmark instances. Furthermore, we present a comprehensive case study examining a medium-sized French municipality, through which we demonstrate the practical integration of real-world design principles within our optimization framework. This empirical analysis yields novel insights regarding the sensitivity of both our proposed parameters and commonly employed parameters in bus network design literature.